An interesting and fair question, though my advice is not to worry!
It is true that servers go through a "life cycle". On a new server, there are many folk at your level, that is true. However...
* there are no high level characters to buff and lend a hand
* there are lots of people chasing YOUR spiderling
* there are NO nice items from high zones for sale in the bazaar
* there are NO grand master jewellors or bakers etc around to help with a tricky combine.
* there may or may not be others on who can advise you on quests or class questions.
* there will not be a choice of guilds (raiding, family, single purpose etc).
So really, mature servers are better in many ways.
You WILL meet other new players. However, you often be grouped with "alts"... characters owned by higher level players. They will be at your level, but may have better gear. They will likely also know what they are doing. You can be depressed by this, or USE IT. Learn from them, and level up with them.
My main is now a lvl 56, and I have enjoyed bringig him up over the last year or so... it is hard to explain how VAST and OPEN everquest is.. you will appreciate the many tips and suggestions from more experienced players.